Modeling nonlinear bending of axisymmetric circular nano-plates in framework of Ru’s surface stress elasticity theory

The nonlinear bending of axisymmetric circular nano-plates is investigated in the framework of the Ru’s surface stress elasticity theory. The inside behavior of the nano-plate is modeled as Kirchhoff plate taking into account the von Kármàn geometric nonlinearity. On this basis, a system of nonlinear ordinary differential equations coupling the in-plane component of the displacement vector and the deflection results from equilibrium equations. We point out that, the differential equation of the deflection is uncoupled from the in-plane one. Afterwards, a simple semi-analytical solving is developed. We have shown that, the normalized deflection is sensitive to the aspect ratio, i.e. (h/a); and no significant difference has been highlighted between the predictions of the present modeling and those arising from the Gurtin–Murdoch (GM) surface elasticity theory. Moreover, results of the FE-simulations reveal that predictions are reliable for appropriate values of the aspect ratio and inflating pressure. Overall, the present work provides a relatively simple computational method of deflections, moments, and symmetric membrane forces in the framework of circular thin nano-plates.